# Gravitationally trapped photons leads to quantized space-time

• johne1618
In summary, the conversation discusses the concept of a photon getting trapped in its own gravitational field and the equations used to calculate this phenomenon. It also delves into the idea of spacetime area and how it is quantized for a bound photon. The speaker also mentions the need for new physics at the Planck level and warns against using Newtonian theory for both light and general relativity.
johne1618
Hi,

I was wondering what happens if one has a photon that is so energetic that it gets trapped in its own gravitational field.

Imagine a mass m orbitting a large mass M in a circular orbit with radius r and with transverse velocity v. By equating the gravitational force on m with its centripetal acceleration we have:

G M m / r^2 = m v^2 / r

Now let velocity v approach the speed of light c. The mass m will be boosted by a Lorentz factor but I think the equation should still hold so that we have:

G M m / r^2 = m c^2 / r

Thus cancelling m we have:

M = (c^2 / G) r

or in terms of Energy E = M c^2 we have

E = (c^4 / G) r (*)

This is the energy that a photon must have to get trapped in its own gravitational field so
that it orbits in a circle with radius r. The quantitiy c^4 / G is also the string tension so maybe this is also a model of a string.

Now let us suppose that the photon has angular momentum hbar. Then we have

r * p = hbar

where p is the linear momentum of the photon.

Now we know that p = E / c for photons so that we have:

r * E / c = hbar

E = hbar * c / r

E = h * c / 2.pi.r

E = h / t (**)

where t is the time period of the photon orbit.

If we substitute E=h/t into equation (*) we get:

h / t = (c^4 / G) * r

Rearranging we get:

r * t = h G / c^4

Thus we find that the spacetime area occupied by this bound photon, r * t, is quantized.

I was wondering if this is similar to the result that the world sheet area swept out by strings is quantized.

>I was wondering what happens if one has a photon that is so energetic that it gets trapped in its own gravitational field.

That's why we know there is New Physics at the Planck level. The whole world wants to know what happens when a photon's wavelength is smaller than it's scharzchild radius. i. e. at the Planck energy/length.

In addition, the assumption
"'Now let velocity v approach the speed of light c. The mass m will be boosted by a Lorentz factor but I think the equation should still hold so that we have:

G M m / r^2 = m c^2 / r"
.. is not suitable. Transition to special relativity is needed.

The schwartzchild radius r=2MG/c^2 is valid even when general relativity is considered.

A quick example of why mindlessly attempting to apply Newtonian theory to both light and general relativity is inadequate:
From your derviation you would no doubt agree for a circular orbit.
$$v=\sqrt{\frac{GM}{r}}$$
Suppose we want to find the radius of a photon's orbit, so v=c, we get
$$r=\frac{GM}{c^2}=\frac{r_s}{2}$$
Which is inside the event horizon of the black hole! Clearly, something went wrong along the way.

I'm not going to poke holes in everything you've written, but you should realize that your treating GR and photons so lightly is not appropriate.

## 1. What is "gravitationally trapped photons leads to quantized space-time"?

"Gravitationally trapped photons leads to quantized space-time" is a theory that suggests that when a photon (a particle of light) becomes trapped in a gravitational field, its energy and frequency become quantized and limited to certain levels. This, in turn, could lead to the quantization of space and time at a microscopic level.

## 2. How does this theory relate to the concept of space-time?

This theory suggests that the interactions between photons and gravity can have a profound effect on the fabric of space-time. By quantizing the energy and frequency of photons, it could lead to a quantization of space and time, changing our understanding of the fundamental nature of the universe.

## 3. What evidence supports this theory?

Currently, there is no direct evidence to support this theory. It is still a theoretical concept that is being explored and studied by scientists. However, some mathematical models and calculations have shown potential for this theory to be valid.

## 4. How does this theory impact our understanding of gravity?

If this theory is proven to be true, it could greatly impact our understanding of gravity. It could provide a new way of explaining the behavior of gravity at a quantum level and could potentially lead to a unified theory of gravity and quantum mechanics.

## 5. What implications could this theory have for the future of science?

If this theory is confirmed, it could lead to a significant shift in our understanding of the universe and could potentially open up new avenues of research and discovery. It could also lead to advancements in technology and potentially impact fields such as astrophysics and cosmology.

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